Department of Mathematics, University of Leicester, Leicester, UK.
Bull Math Biol. 2012 Sep;74(9):2004-31. doi: 10.1007/s11538-012-9743-z. Epub 2012 Jul 14.
One of the most crucial tasks faced by biologists today is revealing the mechanisms which account for biodiversity, yet we are still far from a full understanding of these mechanisms, and in particular the role of spatially heterogeneous population distributions. Recently, the spatially heterogeneous coexistence seen in cyclic competition models--in which species compete as in the game rock-paper-scissors--has brought them to the fore as a paradigm for biodiversity. Research into cyclic competition has so far been focused almost exclusively on stochastic lattice models with discrete space, which ignore several key dynamical aspects. In particular, such models usually assume that species disperse at the same speed. This paper aims to extend our understanding of cyclic competition by applying a reaction-diffusion Lotka-Volterra scheme to the problem, which allows us to vary the mobility of each species, and lets us take into account cyclic competition with more complex underlying mechanisms. In this paper we reveal an entirely new kind of cyclic competition-'conditional' cyclic competition, with a different underlying mechanism to 'classic' cyclic competition-and we show that biodiversity in communities with cyclic competition in fact depends heavily on the ratios between the species mobilities. Furthermore, we show that this dependence can be completely different for conditional and classic cyclic competition. We also present a wide range of spatiotemporal patterns which are formed in the system, including spiral and target waves, spiralling patches, and irregular chaotic patches. We show that the previously unknown case of conditional cyclic competition is host to a scenario of patchy co-invasion, where the spread of the population front takes place via the formation, splitting and propagation of patches of high species density. This is also an example of invasional meltdown because one competitor facilitates the invasion of the other, but unlike well-known cases of invasional meltdown the co-invaders in this system are not mutualists but antagonistic competitors, and the overall result mitigates, rather than amplifies, the damage done to the native ecosystem.
今天，生物学家面临的最关键任务之一是揭示导致生物多样性的机制，但我们仍远未完全理解这些机制，尤其是空间异质种群分布的作用。最近，在循环竞争模型中观察到的空间异质共存——其中物种像石头剪刀布游戏一样竞争——使它们成为生物多样性的典范。到目前为止，对循环竞争的研究几乎完全集中在具有离散空间的随机格模型上，这些模型忽略了几个关键的动态方面。特别是，这些模型通常假设物种以相同的速度扩散。本文旨在通过将反应扩散洛特卡-沃尔泰拉方案应用于该问题，来扩展我们对循环竞争的理解，这使我们能够改变每个物种的迁移率，并考虑到具有更复杂基础机制的循环竞争。在本文中，我们揭示了一种全新的循环竞争——“条件”循环竞争，其基础机制与“经典”循环竞争不同——我们表明，具有循环竞争的群落中的生物多样性实际上严重依赖于物种迁移率之间的比例。此外，我们表明，这种依赖性对于条件和经典循环竞争可能完全不同。我们还展示了系统中形成的广泛的时空模式，包括螺旋波和目标波、螺旋斑块和不规则混沌斑块。我们表明，以前未知的条件循环竞争的情况下存在斑块共同入侵的情况，种群前沿的传播是通过高物种密度斑块的形成、分裂和传播来实现的。这也是入侵性崩溃的一个例子，因为一个竞争者促进了另一个竞争者的入侵，但与众所周知的入侵性崩溃情况不同，该系统中的共同入侵者不是互利共生者，而是对抗性竞争者，整体结果减轻了对本地生态系统的破坏，而不是加剧了破坏。
